Home Office figures released to the Press Association under the Freedom of Information Act, show that the number of fines has risen from 998 in 2012/13 to 3,319 in 2014/15.

The figures also showed that over the last three years, at least 6,494 stowaways have been found - although the true figure is likely to be far higher.

It comes as the UK and French governments face pressure to end the migrant crisis, which has seen numbers swell in Calais over the summer.

Thousands of migrants have attempted to get to the Eurotunnel and nine have been killed since June.

An estimated 5,000 migrants displaced from countries including Syria, Libya and Eritrea are now believed to be camped in and around the port.

A Home Office spokesman said the increase in fines is largely the result of the growing numbers of migrants at Calais since 2012 rather than a more punitive approach.

Industry body the Freight Transport Association (FTA) said the figures highlighted the growing determination of immigrants to smuggle themselves on board vehicles heading to the UK.

A spokesman for the Home Office said only 7% of those caught were British drivers but too many lorries had insufficient security.

He said: "Most hauliers take their responsibility for vehicle security seriously but, despite co-operation from the British haulage industry, one third of lorries arriving at the UK border do not have basic standards of security.

"The purpose of civil penalties is to ensure that all drivers are taking every reasonable step to stop migrants from boarding their lorries.

"Drivers who have properly secured vehicles will not receive a fine."

The civil penalty fines, introduced 15 years ago, are used in cases where drivers have failed to properly secure their vehicles and carry out checks, rather than organised smuggling attempts which are generally prosecuted in court.

Firms which are accredited with the Border Agency can avoid fines even if stowaways are found on their vehicles, meaning that the true number of stowaways found is likely to be much higher than those recorded in these statistics.

The number of incidents - referred to as clandestine entry cases - has increased at a slower rate than the number of fines issued, rising from 916 in 2012/13 to 1,426 in 2014/15. This suggests the number of stowaways found on each occasion has increased from an average of 1 to 2.3.

In 2013/14 there were 1,625 cases resulting in 2,177 fines.

Donald Armour, manager of the international department at the FTA, said the vast majority of drivers took steps to properly secure their vehicles.

But he said this was becoming increasingly difficult in the face immigrants' determined attempts to smuggle themselves on-board coupled with long queues on the other side of the Channel providing more opportunities to do so.

Mr Armour added: "The problem has definitely increased in recent years and you've got huge numbers of people making a real effort to come across.

"Whereas they used to come in ones or twos, you're now often finding 10 to 20 people smuggling themselves on board at any one time.

"The public ask why drivers don't secure their vehicles better but many go to great lengths to stop this happening.

"You find immigrants getting in through the roof, slashing the canvas sides of lorries or jimmying off locks.

"When you're facing that kind of determination, there is only so much you can do and the only real solution is better control of the immigration situation."

Mr Armour added that not all smuggling attempts centred around Calais. The FTA advises drivers not to stop with 60 miles of a port because of immigrants smuggling themselves on-board at any stopping point.

The Home Office said that a new zone introduced in Calais for UK-bound lorries now provides a secure waiting area for 230 vehicles.

"It is in all of our interests to combat attempts to enter the UK illegally, which can damage the haulage industry financially and place the safety of drivers at risk," the spokesman added.

The Home Office refused to release a break-down of how many fines were issued at each port, saying such information could prejudice law enforcement and immigration controls.